This paper is concerned with two issues that arise in the finite element analysis of 3D solids. The first issue examines the objectivity of various stress rates that are adopted in incremental analysis of solids. In doing so, it is revealed that large errors are incurred by an improper choice of stress rate. An example problem is presented to show the implications of the choice of stress rate. The second issue addresses the need to maintain work-conjugacy in formulating and solving bifurcation buckling problems of 3D elastic solids. Four popular commercial codes are used to obtain buckling loads of an axially compressed thick sandwich panel, and it is shown that large errors in buckling load predictions are incurred as a result of violating the requirement of work-conjugacy. Remedies to fix the errors in the numerical solution strategy are given.
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July 2013
Research-Article
On the Importance of Work-Conjugacy and Objective Stress Rates in Finite Deformation Incremental Finite Element Analysis
Anthony M. Waas,
Anthony M. Waas
1
Felix Pawlowski Collegiate Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
Ann Arbor, MI 48109
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
University of Michigan
,Ann Arbor, MI 48109
1Corresponding author.
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Zdenek P. Bazant
Zdenek P. Bazant
Walter Murphy Professor,
Department of Civil Engineering,
Evanston, IL 60208
Department of Civil Engineering,
Northwestern University
,Evanston, IL 60208
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Wooseok Ji
Research Fellow
Anthony M. Waas
Felix Pawlowski Collegiate Professor
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
Ann Arbor, MI 48109
e-mail: dcw@umich.edu
Department of Aerospace Engineering,
Composite Structures Laboratory,
University of Michigan
,Ann Arbor, MI 48109
Zdenek P. Bazant
Walter Murphy Professor,
Department of Civil Engineering,
Evanston, IL 60208
Department of Civil Engineering,
Northwestern University
,Evanston, IL 60208
1Corresponding author.
Manuscript received April 1, 2012; final manuscript received July 22, 2012; accepted manuscript posted October 10, 2012; published online May 23, 2013. Editor: Yonggang Huang.
J. Appl. Mech. Jul 2013, 80(4): 041024 (9 pages)
Published Online: May 23, 2013
Article history
Received:
April 1, 2012
Revision Received:
July 22, 2012
Accepted:
October 10, 2012
Citation
Ji, W., Waas, A. M., and Bazant, Z. P. (May 23, 2013). "On the Importance of Work-Conjugacy and Objective Stress Rates in Finite Deformation Incremental Finite Element Analysis." ASME. J. Appl. Mech. July 2013; 80(4): 041024. https://doi.org/10.1115/1.4007828
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